The effects of soil bulk density, clay content and temperature on soil water content measurement using time-domain reflectometry

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  • HYDROLOGICAL PROCESSESHydrol. Process. 17, 36013614 (2003)Published online in Wiley InterScience ( DOI: 10.1002/hyp.1358

    The effects of soil bulk density, clay contentand temperature on soil water content measurement

    using time-domain reflectometry

    Yuanshi Gong,1 Qiaohong Cao1 and Zongjia Sun2*1 Department of Soil and Water Sciences, China Agricultural University, #2 Yuan-Ming-Yuan Xi Road, Beijing 100094, Peoples Republic of

    China2 ESI Environmental Sensors Inc., 100-4243 Glanford Avenue, Victoria, BC V8Z 4B9, Canada

    Abstract:Time-domain reflectometry (TDR) is increasingly used for field soil water estimation because the measurement is non-destructive and less affected by soil texture, bulk density and temperature. However, with the increase in instrumentresolution, the influences of soil bulk density and temperature on TDR soil moisture measurements have been reported.The influence is primarily caused by changes in soil and water dielectric permittivity when soil compaction andtemperature varies. The objective of this study is to quantify the influence of soil bulk density and temperature, andto provide the corresponding correction methods. Data collected from sand, sandy loam, loam and clay loam showa linear relationship between the square root of dielectric constant of dry soil and bulk density, and a bulk densitycorrection formula has been developed. The dielectric permittivity of soil solids estimated using this formula is closeto that of oxides of aluminium, silicon, magnesium and calcium. Data collection from sandy loam show a noticeabledecrease in measured soil moisture with increase in temperature when the volumetric soil water content is above030 m3 m3. A temperature-correction equation has been developed, which could provide the corrected soil moisturebased on soil temperature and TDR-measured moisture. The effect of clay content has been detected, but it is notstatistically significant. High clay contents cause the underestimation of soil water content in the low moisture rangeand overestimation of soil water content in the high moisture range. Copyright 2003 John Wiley & Sons, Ltd.

    KEY WORDS time domain reflectometry (TDR); volumetric water content; dielectric permittivity; time delay or traveltime; soil bulk density


    The accuracy of soil water content measurement using time-domain reflectometry (TDR) depends on (1) theaccuracy of time delay measurement and (2) the calibration used to convert measured time delay to volumetricsoil water content. Many techniques have been developed to improve the accuracy of time delay measurement.For example, the switching diode technique has been employed to obtain an unambiguous time mark in theMoisturePoint TDR soil moisture instrument (Hook et al., 1992). Meanwhile, several calibration equationshave been developed to explore the relationship between time delay and volumetric soil water content (Toppet al., 1980; Ledieu et al., 1986; Roth et al., 1990; Herkelrath et al., 1991). Topp et al. (1980) developeda well-known Universal empirical calibration equation between apparent dielectric permittivity Ka andvolumetric water content v. This universal calibration has been validated by numerous reports for twodecades, when it is applied to general soil conditions. However, with the increase of resolution and accuracyof time delay measurement, a discrepancy between Topp et al.s universal calibration and experimental results

    * Correspondence to: Zongjia Sun, ESI Environmental Sensors Inc., 100-4243 Glanford Avenue, Victoria, BC V8Z 4B9, Canada.E-mail:

    Received 21 May 2002Copyright 2003 John Wiley & Sons, Ltd. Accepted 8 September 2002

  • 3602 Y. GONG, Q. CAO AND Z. SUN

    has been reported when the universal relationship of Ka versus was applied to soil with high clay content andsalinity (Dirksen and Dasberg, 1993; Jacobsen and Schjnning, 1993; Dalton, 1992; Wyseure et al., 1997).

    The apparent dielectric constant Ka of a material is determined by measuring the propagating time (timedelay) of an electromagnetic (EM) wave in that material. In practice, an EM wave is sent through the materialof interest along a transmission line (probe) buried in it, and the EM wave is reflected back at the end of thetransmission line. The round-trip time T is then measured. According to Maxwells equation, the velocity v ofan EM wave propagating in a material medium with apparent dielectric permittivity Ka can be calculated thus:

    v D CK05a

    D 2LT


    where C is the velocity of an EM wave in free space and L is the length of the transmission line. Multiplyingby two accounts for a round trip.

    Therefore, the apparent dielectric permittivity Ka is

    Ka D(




    The time delay of an EM wave in air over the distance of 2L is given by

    Ta D 2LC


    Combining Equations (1)(3) we obtainKa D




    or Ka D TTa 4

    The normalized time T/Ta is linked directly to the dielectric permittivity of the material and it will be referredto as the time delay in the rest of this paper.

    As a porous medium, soil consists of materials in three phases: solid soil particles, liquid soil solution andair in soil. The dielectric permittivity of soil, and in turn the measured time delay T/Ta, is a function of thedielectric permittivity of each of its components and the volume fraction of each component.

    The following linear relation between v and T/Ta has been developed by several researchers (Hook andLivingston, 1996):

    v D T/Ta Ts/TaK05w 1


    where Ts is the travel time in dry soil. Similar to Equation (4), Ts/Ta represents the square root of thedielectric permittivity of dry soil. Kw is the dielectric permittivity of the soil solution. By replacing T/Ta andTs/Ta with Ka and Ks in equation (4) we obtain

    v D K05a K05sK05w 1


    Equation (6) shows a linear relation between K05a and v, with slope of 1/K05w 1 and intercept ofK05s /K

    05w 1.

    Ledieu et al. (1986) reported that the calibration equation between Ka and v could be improved byconsidering soil bulk density, although the effects were relatively small.

    Copyright 2003 John Wiley & Sons, Ltd. Hydrol. Process. 17, 36013614 (2003)


    Dry soil consists of solid particles and air. The dielectric permittivity of solid soil particles is in the range25 and the dielectric constant of air is near unity. The denser the soil, the greater the volume ratio ofsolid particles to air, and the larger the dielectric permittivity of dry soil Ks. The intercept of Equation (6),K05s /K

    05w 1, increases with increasing soil bulk density.

    For soil with high clay contents, the bound water effects can not be ignored. The water phase in soil canbe subdivided into a free water phase and a bound water phase. Free water, also called bulk water, is able torotate freely following an alternating electrical field. Its dielectric permittivity is around 80 at 20 C, attributedto its high degree of polarization under an external electrical field. In contrast, the bound water phase consistsof water molecules that are bound to the soil surface by adhesive, cohesive and osmotic forces (Hilhorst et al.,2001). The rotation of bound water molecules following an applied electrical field is restricted, resulting inless polarization compared with that of free water, and a low dielectric permittivity. Or and Wraith (1999)obtained the dielectric permittivity of bound water of 6, 10 and 14 by harmonic averaging for a bound-waterregion made up of one, two and three molecular thicknesses, respectively. Sun and Young (2001) obtaineda value of 302 for the distance-weighted average dielectric permittivity of bound water, which consists offour water-molecule layers from the particle surface (first layer) to free water (fourth layer) in Rideau clay.Obviously, the slope of the calibration Equation (5), 1/K05w 1, will be different for soil containing differentamounts of bound water, which is directly related to the clay content. The magnitude of the difference dependson the amount of clay and the clay minerals.

    The electrical conductivity (EC) of clay soil imposes a great impact on soil water content measurementusing TDR (Topp et al., 1980, 2000; Malicki et al., 1994; White et al., 1994; Sun et al., 2000). The soil ECcomes from the electrolytes in soil solution and the electrical charged clay colloid surface. The elevated ECincreases the apparent dielectric permittivity (White et al., 1994; Sun et al., 2000; Topp et al., 2000), actingcounter to that of bound water in TDR soil water content measurement, and making TDR less sensitive tosoil texture.

    The dielectric permittivity of free water Kw is temperature dependent. The change of dielectric permittivityof free water with temperature can be described by the following formula (Weast, 1986):

    Kwater D 7854[1 4579 103t 25 C 119 105t 252 28 108t 253] 7where t is the water temperature in celsius.

    When the temperature drops from 20 C to 5 C, the Kw will increase from 8036 to 8612, resulting in achange of the slope of Equation (5) from 01256 to 01208. It is clear that the temperature effects must betaken into account for an accurate soil water content measurement using TDR.

    This experiment quantitatively studied the effects of soil bulk density, clay content and temperature on soilwater content measurement using TDR, and attempts to provide practical calibrations for an accurate soilwater content measurement.

    MATERIALS AND METHODThe soils used in this study were sand, sandy loam, loam, silt loam and silt clay. Sand was dug from theriverbed of Xiao QingHe, Beijing, China. Sandy loam and loam were taken from the experimental field ofChina


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